Sedimentation

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Sedimentation
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Most wastewaters and waters contain solids, and
in many treatment processes solids are generated
e.g., phosphate precipitation, coagulation and
activated sludge bioxidation. Particles in water
and wastewater that will settle by gravity within
a reasonable period of time can be removed by
"sedimentation" in sedimentation basins (also
known as "clarifiers").
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Settleable doesnt necessarily mean that these
particles will settle easily by gravity. In many
cases they must be coaxed out of suspension or
solution by the addition of chemicals or
increased gravity (centrifugation or
filtration). Because of the high volumetric flow
rates associated with water and wastewater
treatment systems, gravity sedimentation is the
only practical, economical method to remove these
solids. i.e., processes such as centrifugation
are not economical, in most cases.
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Gravity separation can obviously be applied only
to those particles which have density greater
than water. But this density must be
significantly greater than that of water due to
particle surface effects and turbulence in the
sedimentation tanks. Goals of gravity
sedimentation 1) Produce a clarified (free of
suspended solids) effluent. 2) Produce a
highly concentrated solid sludge stream.
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Review of Type I and II sedimentation

• Type I (Discrete sedimentation)
• Occurs in dilute suspensions, particles which
  have very little interaction with each other as
  they settle.
• Particles settle according to Stokes law
• Design parameter is surface overflow rate (Q/As)

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Type II (flocculent sedimentation)

• Particles flocculate as they settle
• Floc particle velocity increase with time
• Design parameters
• Surface overflow rate
• Depth of tank
• or,
• 3. Hydraulic retention time

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Comparison of Type I and II sedimentation
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Zone Settling Compression (Type III and
IV) Zone settling occurs when a flocculent
suspensions with high initial concentration (on
the order of 500 mg/L) settles by gravity.
Flocculant forces between particles causes
settling as a matrix (particles remain in a
fixed position relative to each other as they
settle). When matrix sedimentation is
constrained from the bottom the matrix begins to
compress. Such a situation occurs when the matrix
encounters the bottom of tank in which it is
settling. This is called compression (Type IV)
settling.
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These settling types are demonstrated in a batch
settling test as illustrated below
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The height of the interface (between the
clarified zone and the zone settling zone)
versus time is plotted in the figure below to
determine the "zone settling velocity" (ZSV).
Velocity of this interface is steady after some
induction period but changes with time as
compression begins. The slope of the steady
interface subsidence rate represents zone
settling velocity.
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Initial suspended solids concentration has a
significant effect on the ZSV because the higher
the suspended solids concentration the more
difficult it is to pass water through the pore
spaces in the settling matrix. (The only way a
matrix can settle is if the water below it is
allowed to pass upward through the matrix). A
typical relationship between initial suspended
solids and ZSV is shown here.
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• Factors affecting zone settling velocity
• Suspended solids concentration
• Depth of settling column (or tank)
• Stirring ( 0.5 2 rpm to prevent arching)
• Temperature
• Polymer addition ( affects matrix structure)

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Design of Zone Settling Tanks
Two important functions of these sedimentation
tanks are clarification and thickening. For a
continuous flow clarifier, operated at
steady-state, mass flow of suspended solids can
schematically represented as follows
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X influent suspended solids concentration Xe
effluent suspended solids concentration (often
close to zero) Xu underflow (thickened)
suspended solids concentration. Q influent
volumetric flow rate Qu underflow volumetric
flow rate
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Batch Flux Method

• The batch flux method is one way to analyze and
  select design parameters for the
  clarifiers/thickeners. Start by considering the
  mass flux of solids through the
  clarifier/thickener. There are two components of
  this flux
• Subsidence (sedimentation)
• Bulk transport (due to sludge withdrawal from
  bottom of tank)

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Total flux of solids through the clarifier is
given by
Where G mass flux (mass of SS
transported/area-time) Vi zone settling
velocity (ZSV) at Xi u bulk transport velocity
due to sludge withdrawal from bottom of the tank.
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u Qu/As Qu underflow rate (withdrawal
rate) As cross-sectional area of clarifier
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Zone settling velocity is highly dependent on Xi,
so to calculate the flux due to subsidence we
need to assume a typical relationship (as shown
above) between zone settling velocity and Xi to
get
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Solid flux due to subsidence (settling) is
calculated by Gs (vi)(xi)
(mass/time-area)
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Flux due to bulk transport is given by Gb
(u)(Xi)
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For a particular u the combined flux looks like
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• For a particular underflow rate u there is a
  minimum in the flux capacity of the clarifier.
  This minimum occurs at Xi XL. (Note there is
  also a minimum G at the origin, but this has no
  relevance since even after the influent X is
  diluted Xi never gets this low). Therefore for
  a given underflow rate there is a "limiting flux"
  which can be transmitted through the clarifier.
  As Xi passes from Xf (suspended solids
  concentration in the influent ) to Xu it must
  pass through this bottleneck Xi XL. This
  controls the solids loading rate to the
  clarifier.

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• Essentially for a critically loaded clarifier
  there exists only two suspended solid
  concentrations, XL and XA if the compression
  zone is ignored. An explanation of "two
  concentration" critically loaded clarifier
  follows. Suspended solids enter the clarifier at
  some initial concentration Xf. These solids are
  diluted by clarified effluent. As the solids
  settle they concentrate and ultimately reach XL.
  

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• Suspended solids cannot be transmitted as fast
  through this layer as in the layers above
  (because the influent has lower suspended solids
  concentration and therefore higher zone settling
  velocity) so there is a build up of suspended
  solids at XL.

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• At steady state the influent suspended solids
  have to be diluted to XA to balance fluxes
  through the clarifier(at steady-state all the
  solids fluxes must be equal at all depths). Any
  other concentrations will cause the layers to
  disappear, either by washing out over the
  effluent or by being drawn through the bottom of
  the clarifier

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When the clarifier is critically loaded. i.e.,
when the loading rate equals the flux capacity of
the clarifier, the resultant concentration
profile in the clarifier is given by
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The batch settling data can be represented by an
exponential function.For example the following
equation is an exponential curve fit to the
settling data shown in the following graph.
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Flux due to subsidence can then be calculated
Be sure to make units consistent. Typical units
kg/m2-hr
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The limiting flux in for each underflow rate, u,
is found by locating the minimum in the total
flux curve. Note that minimum of interest occurs
to the right of the curve peak for reasons
discussed earlier. This minimum can be found
graphically or by differentiating the flux curve
with respect to X and setting the resulting
equation equal to zero and then solve for XL.
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For this particular problem u (m/hr) XL
(mg/liter) 8 11,020 10 10,338 12
9,655
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This means that if we choose to operate a
clarifier with an underflow rate of 8 m/hr
(Qu/As) then the flux limiting concentration will
be at 11,020 mg/L. In other words the subsidence
flux will be
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And the bulk transport flux will be
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The total capacity of the clarifier to transmit
solids under these conditions is
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This same information can be obtained
graphically. In fact once the subsidence flux
curve is drawn a straight line at slope u drawn
tangent to the subsidence curve will give all the
required information. One important point is
that the tangent line must remain below the
subsidence curve otherwise the flux limiting
capacity will be exceeded and the clarifier will
fail.
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Slope 8m/hr
(0.032) Gt
G
(.0075) Gs
(14.41)
11,020
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How is this information used to design a
clarifier? The major design parameters for a
clarifier-thickener are the cross-sectional area,
As, and the volumetric underflow rate Qu. These
parameters must be selected so that the solids
loading capacity of the clarifier-thickener is
not exceeded and the solids concentration of the
underflow is adequate. These parameters can be
selected by the following procedure.
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Consider mass flow through a clarifier
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Perform a solids mass balance around the
clarifier
Typically Xe is approximately zero so the last
term can be ignored.
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The clarifier cross-sectional area and underflow
rate must be selected to satisfy mass balances
and flux capacity limitations. Start with
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Consider the previous case. Assume Qf 103
m3/day and Xf 6500 mg/L We selected an
underflow rate 8 m/hr. This yielded an Xu
14,410 mg/L. Then Qu Lf/Xu 18.8 m3/hr. This
determines As Qu/u 2.355 m2
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The way in which the problem was set up the
clarifier is critically loaded. However,
clarifiers do not need to be loaded critically to
function. For example, the cross sectional area
can be doubled to yield an underflow velocity of
4 m/hr. A mass balance dictates
If Xu is held constant u will be half of the
previous value so Gtotal will be halved.
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Assuming Lf (Qf Xf) is constant then lowering
Gtotal by ½ is exactly compensated by doubling
As. This analysis can be extended to any
combination of changes in Xu, u, Qu, etc. as long
as the mass balance is met and as long as the
line connecting Gtotal and Xu remains below the
subsidence flux curve. In the following graph
black lines are acceptable operating conditions
whereas blue lines are unacceptable conditions.
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There are an infinite number of non-critically
loaded conditions a few of which are shown in
the following graph. All variations in Xu or u or
Gtotal are allowed as long as mass balances are
satisfied.
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Critically loaded design can be accomplished
graphically using the Batch Flux technique.

• Construct a batch flux curve for subsidence
  alone.
• (GS viXi).

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• Select an Xu . Draw a line tangent to the
  subsidence batch curve which originates at G 0,
  X Xu. Extend this line to the ordinate. The
  ordinate intercept is Gtotal. The G value at the
  point of tangency is Gs.

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• The slope of the tangent line is the negative of
  the underflow rate u.

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Gtotal
Gs
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Justification for this procedure can be shown
from geometry or the Kynch analysis.
First use the Kynch analysis. Consider two
layers (at different concentrations and,
therefore, different settling rates) of zone
settling solids. These layers are shown
schematically here.
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X1ltX2 and, therefore, V1 gtV2
The interface between the layers will move
upward with a velocity of U. A mass balance
about the interface gives X1V1 X1U X2V2 X2U
(assuming no accumulation in the interface,
i.e., in out).
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Let G1 V1X1 and G2 V2X2 Then G1 V1X1
G2 V2X2 G2 G1 DG -U(X2-X1) -U(DX) or
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If the system is critically loaded (the downward
bulk transport is equal to the upward U
(propagation of solids upward ) so that the
solids flux is maintained at steady-state in a
downward mode (u U). Or viewed another way the
slope of the subsidence curve at any point gives
the underflow rate (u) necessary to maintain a
critically loaded system at a selected Xu .
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Recall that GL (Gt GL) the limit of solids
loading which can be transmitted per unit area at
a given underflow rate and sludge
settleability. Then
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Tube Settlers One method to increase the
efficiency or increase the capacity of clarifiers
is to install "false bottoms" in the clarifiers.
For example in a rectangular clarifier such a
"false bottom" would look like
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Using Type I settling analysis, the effect of
providing a single false bottom (of equal area of
the original bottom) is to effectively reduce
the critical velocity, Vc , by half if the false
bottom is located at mid-depth. It will be
assumed that particle settling velocity is
vertical (in direction perpendicular to the
original bottom of the clarifier) therefore the
distance a particle need to fall to be removed is
increased by 1/cosq. Where q is angle of
incline.
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If the false bottoms are replaced by a series of
inclined tubes turbulence is minimized
(particularly lateral turbulence) and the
physical integrity of the false bottoms is
increased compared to long flat sheets. Hence the
term "tube settlers". Tube settlers are often
used in retrofit situations.
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